Question

if alpha + beta are the root of the xsquare + 4x + 6 = 0 then the what is the value the Alpha cube +bita cube

Answer 1

$\alpha \: and \: \beta \: are \: roots \: of \: equation... \\ {x}^{2} + 4x \: + 6 \: = 0 \\ now.. \alpha + \beta = - 4 \: \: \: and \: \alpha \beta = 6 \\ { \alpha }^{3} + { \beta }^{3} = \: {( { \alpha } + { \beta })}^{3} - 3 \alpha \beta ( \alpha + \beta ) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {( - 4)}^{3} \: - 3 \times 6( - 4) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 64 \: + 72 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 8$